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PhD Position Statistical Integer Linear Programming in High Dimensions

Research / Academic
Delft

This PhD position lies in the intersection of statistics (high-dimensional techniques) and optimization (integer linear programming) to handle the problems raised by big data. We are looking for a PhD candidate who can develop theoretical and practical tools for analysing and solving complex large-scale optimization problems with data-driven constraints.

Many real-life optimization problems can be modelled and solved using integer linear programming (ILP). However, the input parameters needed for such an ILP are subject to uncertainty because of, for example, estimation errors or unexpected disturbance. In this project, the case is considered where the uncertain input data is high dimensional, which means that the number of available samples of our data is of the same order or even less than the dimension of the uncertain input parameter. For that reason, new statistical techniques need to be introduced for efficiently handling estimation errors in ILPs with high-dimensional input parameters that combine the theory of random matrices, modern shrinkage methods and machine learning.

The developed tools will be applied on problems arising in transportation. When solving flow-based routing problems, part of the input data is a time-varying origin-destination (OD) matrix, which gives the number of trips between each origin and destination. These matrices often include many OD pairs, but for each time step, only a limited number of observations is available. Therefore, the challenge in these routing problems is to design a robust network given the uncertain high dimensional OD-matrices.

The PhD candidate will be jointly supervised by Dr. ir. Theresia van Essen (Optimization) and Dr. Nestor Parolya (Statistics).

Department

Research at Delft Institute of Applied Mathematics (DIAM) is conducted in six research groups: Analysis, Applied Probability, Mathematical Physics, Numerical Analysis, Optimization, and Statistics. Our research on the construction and analysis of mathematical models related to science and engineering is both fundamental and applied in nature and is often inspired by technical and societal challenges. We have, for instance, tackled complex mathematical problems to develop a model for predicting the flow of ash pollution after a volcano eruption. To come up with innovative solutions we maintain intensive contact with other TU Delft departments, technological institutes and research departments.

Besides research, education is an important cornerstone of our department. We teach the Applied Mathematics BSc and MSc programmes, as well as mathematics courses within other programmes at TU Delft, and national programmes such as “MasterMath”. Together with KTH Royal Institute of Technology (Sweden) and the Technical University of Berlin (Germany) we have also initiated the international joint Master’s programme COSSE (Computer Simulations for Science and Engineering).

We value the great atmosphere at our institute and pride ourselves on our sense of community and the spirit of “getting things done together”, which we combine with mutual appreciation for individual success. To foster interaction and cooperation, we organize lunch seminars where colleagues from the various sections discuss their work, and we arrange an annual social activity where all staff members interact informally to get to know each other in a different setting. Our open and transparent way of communicating is reflected in the way we interact with one another and forms the basis for the way we work together to help each other achieve our goals as a team.

Requirements:

  • MSc degree in Mathematics, Computer Science or Statistics/Econometrics.
  • Good writing and presentation skills in English, and certainly proficient in programming.
  • Initiative, drive and ability to setup, organise and execute your research.
  • An affinity with teaching and guiding students.
  • Good organisational skills and ability to work independently and in a team.
  • Strong interest in high dimensional statistics and integer linear programming.

Salary Benefits:

This position combines a 6-year PhD project with teaching responsibilities and includes an official go/no go progress assessment after one year. In the first four years, the expected division between teaching and PhD research is 50/50; in the final two years the teaching load is reduced to 25%. This gives a total of 3.5 years of PhD research, and 2.5 of educational responsibilities.

The primary educational activities will be participating in teaching teams at the bachelor level, co-designing courses, providing lectures, recruiting and managing the teaching assistants, overseeing lab work, and creating and evaluating exercises. Lecturers are in close contact with students, monitor their progress, and pro-actively come up with course improvements. Furthermore, lecturers in a PhD track are involved in supervising bachelor and master students in their research thesis projects, as well as in co-teaching master courses in the area of their research.

Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from € 2395 per month in the first year to € 3353 in the sixth year.
As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

The TU Delft offers a customisable compensation package, discounts on health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. For international applicants we offer the Coming to Delft Service and Partner Career Advice to assist you with your relocation.

Work Hours:

36 - 40 hours per week

Address:

Mekelweg 2